Saturday, January 2, 2016

Bypass & Deflection Effects on Missile Damage

Sorry about the long time between articles.  And for those who watch the BPC YouTube show, sorry I've been unable to come on for the last few weeks.  Holiday season has been a bit busy.  This article has been promised for a while... and here it is!

When the latest generation of missiles (Harrier, Disruption, Blade, and Trident) came out, it was a real resurgence for missile fleets, especially when paired with the Rhino hull.  It wasn't just their DPS/hton, it was also their range and projectile speed that really made them much better than any previous missile. It was also generally recognized that the Blade was the best missile, and the other ones were second class.  A lot of players overlooked the Disruption Missile available in Tier 3 (and still do), but everyone was wanting the Blade.  Because of the bypass on the Harrier and Disrupter missiles, I noticed that Harrier/Disrupter effective damage would overtake the Blade at some high resistance level (in the high 80's), but it wasn't really important in most cases.

Now Kixeye has done a weapon rebalance, and also introduced ships like the Heavy Cruiser and the Draconian Carrier with very high levels of Assault Deflection.  

The weapon rebalance had the following major effects on missile weapons:
Blade - No effect
Harrier, Disrupter, Trident - Damage more than doubled.
Siege, Strike, Achilles - Damage increase and large weight reduction.
Assault - Damage increase and large weight reduction.  Salvo changed to 1 (Z).

I'm ignoring most Forsaken and Reaver (Torrent) missiles for this article.  Most of the Forsaken research weapons have moved down into the really light category, so their performance is more like a Strike Missile, and including them would have just busied up the charts.  I still don't think Torrents are worthwhile in most situations.

Click this link for my more in depth article on the rebalance, and you can see some of the comparisons for missiles I left out.

So after the rebalance, the rest of the "new generation" of missiles really was a lot closer to the Blade, and the previously obsolete Draconian missiles might be usable again. 

Most of the rest of this article is going to be looking at different situations and comparing missile damage.  Those of you who really hate math should probably skip to the charts.  But to understand how I'm computing DPS (and what assumptions went into those charts), I'll remind you of the formula:

DPS = (Damage - Deflection) * Accuracy / Cycle Time

Damage is taken as the primary damage (Penetrative) plus the bonus damage (Radioactive for the Siege Z & Assault Z).  The damage is reduced by the target's resistance against that damage type so damage becomes:

Damage = Pen Damage * (1 - Pen Resist%*(1-Bypass %)) * (1 + Pen Damage Bonus %)+ Bonus Damage * (1 - Rad Resist %)

My spreadsheet uses a ratio of Rad Resistance to Pen Resistance in its computations, but in this article, I set that to 1.0, which effectively makes the Radioactive Resist % equal to the Penetrative Resist %.  This isn't a great assumption because Rad Resist is usually lower, but I couldn't really decide what to set it to.  This does have an effect on the relative effectiveness of the Siege Missile Z & Assault Missile Z that do bonus radioactive damage.

Bypass reduces the effective resistance of your target.  I have confirmed with Doomrooster that bypass does NOT affect deflection.

The Penetrative Damage Bonus is important, because it affects the relative effectiveness of missiles when deflection is included.

Accuracy is the weapon's accuracy multiplied by any accuracy bonuses, and then reduced by the target's evade as follows:

Accuracy = Weapon accuracy * (1 + Accuracy Bonus %) * (1 - Target Evade %)


Accuracy Bonuses can come from the hull, Laser Targeting, or Guided Missile System.  In this article I used only the weapon accuracy for my DPS calculations.  

When comparing the relative effectiveness of missile weapons, the Bonuses & Evade will only have an effect when the net accuracy (after evade) is over 100%.  Since the accuracy can't increase above 100% the DPS increase from an accuracy bonus stops when Accuracy hits 100% , a high accuracy weapon (like the Blade) is helped less by accuracy bonuses when firing at LOW evade targets.  For example, if the target has zero evade, the DPS of the Blade is not helped at all by Laser Targeting because its accuracy is 100% both before and after the LT is added.  (OK actually the Blade's accuracy is 160%, but its HIT RATE is 100% in both cases.) However, a Strike Missile with 60% accuracy will have 96% accuracy after the 60% LT3 accuracy bonus, so its DPS is also increased by 60%.  But against a target with 50% evade, the LT3 Blade ends up at 80% accuracy, it is is helped by LT3.  In most situations (these days), the target's evade is high enough that ignoring all the accuracy bonuses and Evade is good enough to do a relative comparison.

Cycle time is the reload time added to the time that it takes to fire the full salvo of shots. 

Cycle Time = Reload Time + 0.2 * (Salvo - 1)

It is just about always 0.2 seconds between shots in a salvo.  But luckily enough for the purposes of this article, all the missiles I'm comparing have a salvo of 1, so only reload time matters.  This also means that rank-based and weapon reload bonuses don't have any effect on the comparison.

One more number you'll see me use is DPS/hton, which tries to compare the relative usefulness of weapons by dividing by their weight.  

DPS/hton = DPS / weapon weight * 100

Before the weapons rebalance, this number was my most critical statistic in evaluating weapons, because there were drastic differences between weapons.  But since the rebalance, most weapons of a type (like missiles) have had their DPS/hton move much closer together.  In addition, now that missiles are much lighter (mostly), weapon choice isn't as limited by weight, and so raw DPS (rather than DPS/hton) is a much more important statistic.  Most of the comparisons I made in this article are using DPS rather than DPS/hton for that reason.  

So on to the charts...

This first chart will show the relative DPS of the missiles as the target's resistance increases.  It assumes no damage bonuses and no deflection.



When plotting my data, I used the convention that the base weapon was plotted with a solid line, and the R15 version uses a dashed line.  Most of the missile retrofits increase damage or fire rate, but the Bypass Missile retrofit increases the bypass percentage.  Because of this, there is no difference in those missiles' (the Harrier, Disruption, and Achilles) performance against a target with zero resist, but the difference shows up as the target resistance increases.

Also note that the DPS statistics for the Harrier and Disrupter are the same, so I used a single line to represent both missiles.

Most of the weapons have their damage trail off toward zero except the ones with some significant deflection - the Harrier / Disrupter (shown on the same line since they so the same damage), the Achilles, and the Strike B.  Those weapons have bypass which allows them to ignore a percentage of the resistance.

The Trident (orange) is often forgotten about because of its short range, but when used on a remote targeting ship it can be effective, although its damage won't be as good at those remote ranges.

The crossover points in the lines are important.  For example, the Blade R15 (yellow dash) line crosses the Disruption R15 (brown dash) line at around 64%, meaning the retrofitted Disruption (or Harrier) does more damage than the retrofitted Blade against targets with more than 64% penetrative resist.  If not retrofitted, that crossover point is at 55%.

The same graph showing DPS/hton is below:


  
The graph looks a lot more crowded, because of what I said before - Kixeye made a lot of the weapons perform much more closely to each other (in DPS/hton) after the rebalance.  

On that chart, the Harrier (red) shows much better than the Disruption (brown), since it weighs less, but the real surprise is the strong showing of the Achilles Missile (gray), which is quite possibly my least favorite weapon in Battle Pirates ever.  Of course, its high efficiency in DPS/hton is mostly because they have made the weapon lighter.  So a Mastodon full of Achilles Missiles still won't be as good as a Mastodon full of Blades (at least until Pen resistance is above 92% or so - see the last chart).  It won't ever be as good as a Mastodon full of Disruptions or Harriers.  And Kixeye still hasn't fixed build times, so that Mastodon full of Achilles will take an obscene amount of time to build.  Don't do it.

The interesting bit is that you can see that the Blade R0 and the Harrier start in the same place. In other words, the Harrier & Blade have identical DPS/hton, and so against a target with any resistance, the Harrier will be more efficient.  When fully retrofitted, that crossover point is around 33% resistance.

We have all come up against ships with Assault Deflection that reduce incoming damage.  The Proto-Hunter has 60 Assault Deflection, The Heavy Cruiser has 300, and the Draconian Carrier has 450.  This reduces damage per hit, and it isn't affected by bypass, so that will favor the higher damage missiles, as you can see on the graph below.



Two Notes:
1. I have not been able to confirm if there is a minimum damage that comes into effect with deflection.

2. The "hockey stick" at the bottom of the charts are an effect of doing the calculation at every 5% damage point.  The lines should actually be straight.

Many of the missiles are completely ineffective against the 450 deflection from a Drac Carrier.  When considering that a Drac Carrier using D5-X Compound Armor R0 is at 53% Penetrative Resist already (59% with R15), even an unretrofitted Blade is pretty much useless. 

I think the unexpected result is that the Siege Missile Z shows up pretty strongly here compared to the other missiles.  The reason is that it has a higher base damage than any other missile (1943 damage at R15 including the Bonus damage, a Blade R15 does 1255 damage).  When deflection is not at work, its lower accuracy makes its DPS worse than the Blade, but the higher starting damage helps it against the high deflection ships. 

But there is another factor at work here - damage bonuses.  If you are using a Rhino, you get a 20% damage bonus, and many players will use Enhanced Warheads, Strike Warheads, or Interception System with their missile ships.  EW3 gives a 33% damage bonus, SW & IS gives a 45% damage bonus, and SW R15 gives a 55.7% damage bonus.

Without deflection, the crossover points on the charts are just scaled when considering these damage bonuses, since they just scale the DPS.  But against the Drac Carrier they look like this:



Now the missiles look a lot closer to each other, especially in that range around 50% - 60% penetrative resist that we would expect from a Drac Carrier.  The Harrier and Disruption missiles stay relevant against high resistances.

So what have we learned?

The "Best" missile really depends on the situation.  

In my personal case, I am using two remote targeting ships in my Guard fleet.  One is a Proto-Mastodon with all Harrier Missiles, and the other is a Mastodon with a mix of Siege Z & Strike L missiles.  Both have EW 3. As you can probably deduce, my guard fleet updates tend to lag my other ship builds (since i much prefer spending my shipyard time building ships I sail around & have fun with), however, I was planning to refit the Mastodon with Blades.  After running these numbers, I think I will keep the Siege Z missiles, and only refit over the Strikes (probably to Blades to keep a mix).

Another point this analysis should have really driven home for many players is that if you haven't gotten Blades or Harriers, Disruption missiles are a great option.  If using Harriers or Disruption, the Bypass Missile retrofit is relatively cheap, so that is a cost-effective use of Uranium.

Keep range in mind too.  Although Tridents look great in these damage comparisons, their range with SFB3 is only 71.5  Even the difference with Siege Missiles (88.4) and Blades (98.8) is very significant, and is a big factor in making the Blade/Harrier/Disruption missiles more effective.

The Achilles is starting to show up OK in these missile comparisons, but keep one more statistic in mind... 2 days, 27 minutes, 29 seconds.  That's the build time of ONE Achilles Missile (with officer).  It was a terrible deal when new, and it still is.  Look at the Siege Z at 15 hours each, or even the Cutlass 4 at 10 hours 45 minutes (if you're really hurting for missile options).  Although the weapon rebalance seemed to have a goal of making a lot more weapons 'usable', build time reform is sorely needed before that is really the case.

One more thing - if you want the spreadsheet I used to generate these plots, you can download it at:
https://onedrive.live.com/redir?resid=C9A8A15DF32CF33F!668&authkey=!AJqvJtJm8tTWoPk&ithint=file%2cxlsx
(Whoops! had an editable link posted for a while there.  Hopefully nobody messed with it too much, and any errors are now clearly the fault of the random dudes who messed with the spreadsheet.  Ha ha no I think it's still good.)

Hopefully you guys won't find any errors...but if you do, please let me know.